Answer:
4512.
Step-by-step explanation:
We are asked to find the number of five-card hands (drawn from a standard deck) that contain exactly three fives.
The number of ways, in which 3 fives can be picked out of 4 available fives would be 4C3. The number of ways in which 2 non-five cards can be picked out of the 48 available non-five cards would be 48C2.
[tex]4C3=\frac{4!}{3!(4-3)!}=\frac{4*3!}{3!*1}=4[/tex]
[tex]48C2=\frac{48!}{2!(48-2)!}=\frac{48*47*46!}{2*1*46!}=24*47=1128[/tex]
We can choose exactly three fives from five-card hands in [tex]4C3*48C3[/tex] ways.
[tex]4C3*48C3=4*1128=4512[/tex]
Therefore, 4512 five card hands contain exactly three fives.
